tl;dr "Discoverability is cut almost in half by hiding a website’s main navigation. Also, task time is longer and perceived task difficulty increases."
I have an (admittedly ancient) Android smartphone in my pocket which has dedicated physical menu and back buttons. I don't recall seeing hamburger menus until phone manufacturers started being too cheap to include that menu button.
Now they're everywhere, even (especially) when they're not remotely appropriate. What could be more ridiculous than a touchscreen-oriented menu button in a text editor (looking at you, Gedit) or a VCD waveform viewer (looking at you, GtkWave)?
Enlarging the menu so its easier to find with screen reader tools like TalkBack and VoiceOver has been somewhat effective. However, if you have split menu's, login, search and other features, you start running into complex design issues with where to put all of those and whether you want to stuff them all in the mobile menu, outside the menu or a combination of the two. When you start putting features like search and login into the mobile menu, that also creates more accessibility issues as well.
Designing for accessibility can get really complex, really fast and I'm not sure there's really a solid design pattern yet that addresses all of the issues we're seeing now.
I know that's not a great answer, but it just highlights the complexity of designing for accessibility.
BigCorps Inc. don't like these, because each menu choice has 3 departments and 14 sub-departments that mate-guard their particular menu area, so designers just give up on mobile and hide it all behind the hamburger icon.
It's absolutely daft. Your Web site should be an extra employee, never-tiring, always at work, facilitating the customer or visitor's needs. It's really weird, but depressingly predictable.
The other issue is the placement of the menu in the upper right or left hand corner is nearly impossible to find with TalkBack or VoiceOver controls. Sometimes even with aria attributes, you really have to search with your finger to find the menu and interact with it.
When you use VoiceOver for example, an easy test is dragging your finger down the middle of the screen, you should be able to access the majority of the content - when the menu is tucked too far up in the corner, or too small, it gets obscured by the logo, CTA or anything else that's in the area and gets bypassed by VoiceOver.
Making it large enough to find by simply dragging your finger down the middle of the screen is a good enough test to determine if its big enough, too small or located somewhere it would be skipped by those screen reader tools.
Hope that helps.